Question

In how many ways can the letters of the word “CAT” be arranged?

• A. 3
• B. 6
• C. 9
• D. 12

Hint:

If a word has repeating letters (like "MOM"), you must divide by the factorial of the number of repeats. For "MOM", it would be $\frac{3!}{2!} = 3$ ways.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The number of ways to arrange $n$ distinct objects is given by $n!$ (n factorial). This is a problem of permutations where the order of letters matters.

Step 2: Identifying the Values:
The word "CAT" has $n = 3$ distinct letters (C, A, and T).

Step 3: Calculation:
The number of arrangements is $3!$: \[ 3! = 3 \times 2 \times 1 = 6 \] The actual arrangements are: CAT, CTA, ACT, ATC, TAC, TCA.

Step 4: Final Answer:
The letters of the word “CAT” can be arranged in 6 ways.